Crystals of the apatite group are prevalent in nature. The mineral apatite itself, typically close in composition to Ca10(PO4)6F2, is widely disseminated as an accessory phase in all classes of rock, i.e. igneous, sedimentary, and metamorphic (C. S. Hurlbut, Jr., et al., Manual of Mineralogy, 19th ed., John Wiley and Sons, (1977)). A wide range of synthetic crystals of the apatite group have been studied for their potential usefulness as laser ceramics. Single crystals of Sr10(PO4)6F2 (“SFAP”), or Sr-fluorapatite, have been evaluated as Yb-doped solid state laser crystals (L. D. DeLoach et al., J. Opt. Soc. Am. B, 11:269-76 (1994)). Other Yb-doped apatite crystals are also being investigated as laser materials, such as Yb:C-FAP [Yb3+:Ca5(PO4)3F]. What is needed are single crystals of the Yb-doped apatite crystals, and methods for making them. Surprisingly, the present invention meets these, and other needs.